This revision prevents impossible cam schedules and removes a variable-length lever drawing and unsupported high-speed performance claims. A closed barrel-cam groove captures a follower rigidly connected to the guided shuttle through a valid cycloidal forward-dwell-return cycle.
Closed-Groove Positive Shuttle Schedule Explorer
Enter cycle rate, stroke, forward angle and far-dwell angle. The constrained ranges always leave at least 30 degrees for return; the worksheet applies zero-boundary-velocity cycloidal motion to both strokes.
Equation Used
- One barrel-cam revolution produces one complete shuttle cycle.
- Forward, far dwell and return are the only segments and their angles sum to 360 degrees.
- Forward and return use full-cycloidal displacement with zero velocity at segment boundaries.
- The follower is captured by a closed groove and its carriage is rigidly connected to the guided shuttle.
- Animation phase represents constant cam angular speed and the displayed shuttle displacement follows the declared program.
- Cam diameter and width, groove/roller geometry, pressure angle, curvature, undercut, clearance, contact stress, lubrication, mass, force, deflection, vibration, backlash, wear, manufacturing tolerance, life, drive torque, controls and safe operation are excluded.
Guarantees a valid 360-degree schedule, applies exact cycloidal forward/return motion and replaces the variable-length lever with a captive closed-groove follower.
A closed groove positively constrains both strokes
A roller on a guided follower block runs inside a closed track on a rotating barrel cam. Because both sides of the groove constrain the roller, rotation can command forward travel, hold the far position and command return without a separate return spring. A rigid carriage connects that follower to the shuttle.
The animation shows the exact declared displacement program beside the captive physical follower and guided shuttle.
Use this page to audit a declared motion schedule
The worksheet can verify that angles and times form one cycle and inspect a smooth normalized displacement. It cannot size or manufacture a cam, select a follower or predict performance under load.
Partition the revolution before evaluating displacement
The allowed inputs guarantee beta_r is at least 30 degrees, so every cycle contains a forward segment, optional far dwell and positive return.
This full-cycloidal forward law starts and ends at zero velocity. The return uses S[1-u+sin(2 pi u)/(2 pi)], also meeting its boundaries at rest.
A transparent declared schedule
At 300 cycles/min, one revolution takes 200.0 ms. A 120 degree forward segment takes 66.7 ms, a 60 degree far dwell takes 33.3 ms and the remaining 180 degree return takes 100.0 ms. Declared stroke is 120 mm.
This is a kinematic program, not a claim about feasible speed, load or accuracy.
A displacement law is not a finished barrel cam
Detailed design still needs cam diameter and width, roller size, groove offset, pressure-angle and curvature checks, undercut avoidance, contact stress, materials, lubrication, clearances, manufacturing tolerances, drive torque and dynamic analysis.
The former universal production speeds, sub-millimetre repeatability, specific machine deployments, hardness, life, load, clearance and failure claims are removed because they were not sourced to a tested mechanism.
Positive-shuttle schedule questions
Why can the angles no longer exceed 360 degrees?
Forward and dwell ranges always reserve at least 30 degrees for return.
Why use cycloidal motion?
It joins dwell segments with zero follower velocity.
Does a closed groove eliminate all backlash?
No. Real clearance and compliance are excluded.
Can this generate a manufacturable groove?
No. It defines displacement only.
Positive-shuttle references
- Ohio University ME 301: rise/dwell/return events and full-cycloidal displacement law.
- NASA NTRS 19900017005: full-rise/full-return cycloidal cam equations.
- US Patent 4,042,148: guided follower block, push-pull rod and roller in a rotatable barrel-cam groove.
- US 2019/0063413: closed-loop barrel-cam track converting rotation to reciprocation while confining the follower.
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